We checked the situation with a fresh setup again and a simple update in Jivelite (pre-compiled by Max2Play) solves the issue. You also have to make sure that the Screensaver settings are set to „blank screen“ when off and when paused. This should get the trick done.
Nonetheless, we appreciate the DIY solution and will continue to link to it if other users experience similar issues. Thanks for your detailed contributions and for pointing out this problem.